MULTICOMPONENT FRACTIONATION Distribution of Three Comnonents J. J. HOGAN, Arthur G. R.IcKee 82 Company, Cleveland, Ohio
For multicomponent rectification, a method is presented to determine the distribution of three components of the feed between the overhead and residue at total reflux and at minimum reflux. A new method for the calculation of minimum reflux in multicomponent fractionation is developed. Examples are presented which illustrate the method of determining the minimum reflux and the results are compared with other recent methods. An example is also given showing the calculation of the distribution of three components of the feed.
T
HIS paper is primarily concerned with the fractionation of a multicomponent mixture where three components of the feed are distributed between the overhead and bottom products. Such a fractionating condition may exist when a separation is desired between propane (approximately -40" F. normal boiling point) and n-butane (approximately +30" F. N. B. P.) in the presence of isobutane (approximately + l o " F. Y. B. P.). With both the former components distributed between overhead and bottom product, the intermediate component normally is also so distributed. A slightly different case is the fractionation between isobutane and isobutylene (approximately + 2 6 O F. N. B. P.) in the presence of n-butane. Under some conditions the adjacent component, n-butane, may also be distributed between the two products. Consideration here is limited to the two extreme cases of minimum reflux and total reflux (minimum decks). The well-known relation developed by Fenske ( 2 ) for total reflux with two components may be readily applied t o three components. However, it is necessary to present an approximate method for the calculation of minimum reflux which differs from those methods previously presented although derived from essentially the same basic considerations, in that it is based on observation of the results of standard plate-to-plate calculations. Assuming that a plate-to-plate calculation is started with the overhead product a t the top of the column, it is found that the ratio of the quantity of light key component to the quantity of heavy key component (key component ratio) decreases as the column is descended. However, for a definite reflux ratio there is a limiting value to the key component ratio; after a sufficient number of plates there is prac-
tically no change in the quantity of any component from one deck to the next. Thus a zone of no fractionation is reached. Further, the higher the value of the reflux ratio, the lower is the limiting value of the key component ratio. If for a given overhead stock we desire to reach a certain key component ratio, it is possible t o find by trial and error a reflux ratio which will just permit reaching the chosen key component ratio. Higher reflux ratios allow passing through the chosen componFnt ratio to lower values; lower reflux ratios cause the fractionation to stop before the chosen component ratio is reached. A corresponding condition exists below the feed. It is now apparent that if, for a given feed and degree of fractionation, the key component ratios were known a t the bottom of the enriching section and the top of the stripping section, it would be possible to obtain the minimum reflux ratio by trial and error. For a finite column Gilliland (3) developed the limiting value which is t o be approached by the key component ratio above and below the feed. For a n infinite column it may be assumed that this ratio is reached on the feed plate and on the plate above the feed. Thus, the minimum reflux ratio for a multicomponent mixture can be calculated. However, it is apparent that a method as outlined above which requires several long plate-to-plate calculations would be entirely too time consuming for normal use. (Also, there can be considerable difficulty with such calculations in the feed zone between the two zones of no fractionation.) Accordingly several shorter methods have been developed for approximate determination of the minimum reflux ratio. The published methods will be reviewed before presenting the different methods found useful in determining the distribution of a third component. Gilliland (4) recently modified the method presented by Robinson and Gilliland (7). The modified method comprises two cases. I n case I allowance is made in each section of the column for all constituents of the feed, and it is assumed that the concentrations of all components are the same on the feed plate and the plate above the feed. As a criterion the key component ratio mentioned above ( 3 ) is used. The minimum reflux can be determined from either of two algebraic relations which the present author has found simple, rapid, and adequate in normal cases of fractionation having only two distributed components which are reasonably different in volatility and are of normal volatility. For fractionation of components close in volatility, the relations are sensitive to the temperature chosen for determining the relative volatility and there is no automatic check on this temperature. (For conservative design it is best to use the volatility a t the still temperature.) I n case I1 no allowance is made in one section of the column for components which do not appear in the end product from that section. For this case a criterion has, been proposed which is a modifictttion of that used in case I.
1132
September, 1941
INDUSTRIAL AND ENGINEERING CHEMISTRY
I have found this method less satisfactory to use than that derived from case I since the sensitivity to temperature is much greater, and as before there is no automatic check on the assumed temperature. Considerable difference can result above and below the feed if the appropriate temperatures are not used. Gilliland notes that the results from case I are usually above the true minimum reflux, and those from case I1 are usually below the true minimum. Neither case, however, offers a clue to the distribution of a third component. Brown and Martin ( 1 ) proposed a method which is similar to case I1 of Gilliland, since in each section of the column allowance is made for only the components present in the end product from that section. Brown and Martin’s criterion is the feed ratio of the key components modified for various conditions of the feed. This method may, for a given separation, be applied separately to the upper section of the tower and to the lower section, and in each case an automatic check is provided on the assumed temperature. I n many cases approximately the same minimum reflux ratio is obtained from the two applications; it can happen, however, that this agreement is not obtained, and therefore it is always necessary to make the two separate calculations. The method gives no clue t o the distribution of a third component. Jenny (6) published a method which differs considerably from those described above and is seemingly closer to actual plate-to-plate calculations. Allowance is made for all constituents of the feed. Further, allowance is made for fractionation between the feed plate and the plate above the feed. Two criteria are used: Above the feed the criterion is the concentration of the heavy key component and below the feed it is the concentration of the light key component. I n the approximate method, concentrations on the feed plate and the plate above are assumed to be the same as in the corresponding zones of no fractionation. To obtain really satisfactory results, the more precise method requiring plate-toplate calculations between the two zones of no fractionation is necessary. Although this method seems to account well for the phenomena which occur, i t requires trial and error in the plate-to-plate calculations. There is a further complication in that a t the start it is necessary to assume, independently of each other, the temperature of the feed plate and of the plate above although these assumed temperatures can be checked. Considering a third distributed component, Jenny has limited his discussion to a finite column; while it is possible that the method might be extended to an infinite column, it will.be shown that a simpler method can be followed. The method to be presented here is of the same general type as those mentioned above but differs in a t least one poipt from each. Allowance is made for all constituents of the feed and for fractionation of components other than the key components between the feed plate and the plate above. The criterion is the ratio of the key components, and it is assumed that this ratio is the Bame on the feed plate and the plate above. As will be shown later it is readily adaptable to the determination of a third component. The method here presented is more like that of Jenny (6) than like those of the others; it differs from Jenny’s chiefly in the use of a ratio rather than a concentration as a criterion.
1133
If there is no fractionation from deck to deck, the customary material balance and equilibrium expressions result in ad Above feed: 1, = K, - a Below feed: I ,
bw b - K, whered = moles of an individual component in distillate 1 = moles of an individual component as liquid in tower w = moles of an individual comDonent in residue K = a b
=
= =
L =
v = total moles of vapor in tower n = conditions in upper section of tower m = conditions in lower section of tower For those unfamiliar with the use of molal quantities rather than molal fractions, the following derivation of Equation 1A may be useful. Counting decks from the top of the tower, a material balance in the enriching section is I, = vTL+ 1 - d. On deck ( n
+ 1) the equilibrium relation is Vn - = +1
V
Kn + 1
[‘?I
When there is no fractionation, conditions are the same on deck n as on deck (n 1); consequently, the value of v from the above equation can be substituted in the preceding:
+
which yields Equation 1A.
Minimum Reflux with Two Distributed Components For simplicity in presentation, the development of the method for minimum reflux will first be made with the implied assumption that there are only two distributed components. Further, at present the development will be limited to the case of a feed which enters the tower as liquid a t the feed plate temperature. The usual simplifying assumptions are made.
Courteay, Arthur Q. McKee & Company
GASOLINE STABILIZATION UNIT
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1134
It is apparent that the quantities of heavy components in the liquid above the feed cannot be calculated b y Equation lA, and similarly the quantities of light components in the
Vol. 33, No. 9
As noted above, it is assumed that the value of rc is the same on the feed plate as on the plate above. It is important that the values of a and b given by Equations 6 are those which satisfy the condition that the ratio of the key components shall be re a t the feed plate and a t the plate above the feed. For convenience Gillilaud’s criterion ( 3 ) for feed plate location for the particular case now being considered is given below:
liquid below the feed cannot be calculated b y Equation 1B. By assuming that the quantities apply t o adjacent plates in the tower and that the quantities in the lower section exist on the feed plate, the required quantities can be obtained by material balance and equilibrium relations. T o determine the quantity of a heavy component in the upper section, the material balance is made around the top of the column and just above the feed; to determine the quantity of a light component in the lower section, the material balance is made around the bottom of the column and just above the feed. It is assumed in this case that 1, = 1, f. These material balances combined with the equilibrium relation at the feed plate result in
Tc
.flk/fhk
(7)
All the interlocking relations having been obtained, it is now possible a t a given reflux ratio to calculate the quantity of each component of the feed on the feed plate and on the plate above the feed. This can be done for any chosen reflux ratio; the correct reflux ratio is that a t which
+
2L = L, 21, =
L,,
(84 (8B)
Procedure
T o determine the quantities of every component of the feed either on the feed plate or the plate above, i t is necessary t o know both a and b. These cannot be chosen individually since they are associated values. To determine the relation, total material balances are made first around the upper section and then around the lower section of the tower, resulting in:
Assuming that the overhead and residue compositions and the tower operating pressure and temperatures have been establishcd, the procedure below is followed : 1. Calculate the values of T ~ T, D , and rw. 2. Calculate and plot against temperature the values of a and b (Equations 6A and 6B). 3. Choose a temperature for the plate above the feed (t,) and determine a from the plot. Calculate the associated value of b (Equation 5B) and determine the feed plate temperature (t?). If t, is not higher than t,, repeat with a lower value
Above feed: L, = aD/(l - a ) Below feed: L, = bW/(b - 1) where D = total moles of distillate W = total moles of residue
4. After a logical pair of temperatures has been obtained, calculate L, (Equation 3A). 5. Calculate the values of I , (Equations 1A and 2A) and from them, 21,. 6. Repeat until Equation 8-4is satisfied.
wheref = moles of an individual component in feed h = component heavier than heavy key component 2 = component lighter than light key component
By a heat and material balance around the feed plate,
’
(4)-
where F = total moles of feed Combining Equations 3A and 4 and Equations 3B and 4, a = (F bD)/W b = (F - a W ) / D
-
In addition to knowing the associated val also necessary to know the associated values of Kn and K,. These equilibrium constants can be related indirectly through the associated values of a and 6. Above the feed, Equation 1A is applied separately t light key component and to the heavy key component to in the moles of each component on the plate above the feed. Dividing the expression for the light key component b y that for the heavy key component results in a n expression for the ratio of these components on t h e plate above the feed. The ratio of the key components in the distillate also appears. Similarly, b y applying Equation 1 B to both key components, a n expression is obtained containing the ratios of the light key component t o the heavy key component on the feed plate and in the residue. The expressions are :
where r k c
D W
=F
= = = =
‘ra.8cib) of light to heavy key component key cbmponent criterion conditions distillate conditions residue conditions
of t,.
(3‘4) (3B)
The following notes on the method of procedure will help to reduce the time consumption: Frequently K I L h k is so close to a that there is no precision in calculating l n h k by Equation 1A. It is correct t o calculate l n h k as
lndrc. If ZZ, is less than L, the assumed value of t, is too high, and the next trial should be made at a lower temperature. A guide to succeeding approximations is that 21, is closer to the correct value for the total liquid in the tower than is L,. , A check on the work can be made by calculating the values of 1, and determinin whether Equation 8B is satisfied. L, can be calcuyated by Equation 3B or 4. This provides an intermediate check on the associated values of a and b. It is possible to start with an assumed value of t,; however, it is necessary t o calculate first the values of I,.
At times a satisfactory solution cannot be obtained. This indicates that the distribution of a third component has not been assumed correctly. The second section of this paper outlines the procedure t o be followed.
It is recognized that the above method contains certain inconsistencies. Thus, in the upper section of the tower the quantities of the heavy key and lighter components are calculated on the basis of no fractionation. Then to the quantities so calculated are added quantities of heavier components which invalidates the assumption of no fractionation. Further, it is not possible to prove t’hat the two compositions assumed to exist on adjacent plates can actually be so located. However, such inconsistencies are not surprising in a n a p proximate method and the value of the method can be judged only on the basis of the results. The method here proposed, used in conjunction with the empirical methods to determine actual plates and actual reflux ratios proposed by Brown and Martin ( 1 ) or by Gilliland (6) has been found satisfactory. It is probable that at least a partial reason is the use of a ratio of components as a criterion.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
September, 1941
Distribution of Three Components at Minimum Reflux As noted above, it is possible to have three components of the feed distributed between the distillate and residue when a desired separation is established between two of these components. I n the following discussion the three components are classified as the light key component, intermediate key component, and heavy key component, and are identified by subscripts I, i, and h, respectively. I n any particular case the desired distribution of any two of these components will be known and that of the third is to be calculated. As is the case when only two components are distributed, the ratio between any two of the three components is given by Equation 7 a t the feed zone. Equations 6A and 6B may then be written for any pair of the three distributed components, and the three resulting expressions for a or b can be equated:
( K n h k ) (TDlhk) TDlhk
- (Knlk) - Tclhk
(Tclhk)
(9-4)
for which the general solutions are
=
U U ( D- B ) v(D -A)
uv ( D u(C
- UY
(C
- B)
+ y (A - C)
tn, the associated values of b and tm and proceed if t, is greater than t,. 4, 5, 6. Same as before.
From Equation 13 it is apparent that for a given feed stock there is a value of T D l i k above which there can be none of the heavy key component in the distillate because the bracketed term would be negative. If desired, this minimum value can be determined by equating the terms within the bracket and solving for T D l i k .
Distribution of Three Components at Total Reflux At total reflux Fenske ( 2 ) developed a relation which is generally applied to the distribution of two components of the feed:
where N = number of decks CY = relative volatility
It is apparent that any two of the above expressions when equated are of the form:
'=
1135
(11)
- B ) - vx ( D - A )
This relation can be applied to any pair of the three distributed components to yield three expressions which must be equal. By equating two of these, the distribution of a third component can be calculated.
Application of the Method EXAMPLE 1. The following example is given to show the accuracy of the proposed method. Gilliland (4) gives a probem in which all components of the feed are present in the residue and thus permit the determination of the minimum reflux ratio by plate-to-plate calculations without difficulties in the feed zone. The minimum reflux so calculated is 4.82/1. The difference between this value and that determined by Gilliland is ascribed to the difference in vapor pressure data. This desired fractionation is indicated by the material balance. The operating pressure is 250 mm. of mercury absolute:
- B) + x ( A - C)
By Equations 11 and 12 the ratio of any two components in the overhead or residue can be obtained from Equations 9A and 9B. As an example it will be assumed that the distribution of the light and intermediate key components has been established and that it is desired to know the distribution of the heavy key component. This means it is necessary to know TDlhk or TDihit or the corresponding ratios in the residue. Examination shows that if the second and third terms of Equation 9A are used, all the ratios include the heavy key component. Therefore it is necessary to use the first and second terms or the first and third terms. From the first and third terms,
Phenol o-Cresol m-Cresol Xylene Residue
1oo.o
33.1
.... ..
Residue 3.5 13.4 30.0 15.0 5.0
es.s
= 35/15 = 2.33; T o = 31.5/1.6 = 20.3; TW
-
tm
-
-
Assume tn = 149' C. (300.2" F.); a = 0.820; b = 1.364; 154.2" C. (309.6" F.); Ln = 150.9; L m 250.9:
Phenol o-Cresol 'w-Cresol Xylene Residue
1, 2. Same as before. 3. Choose value oft,, and determine theborresponding distribution of the third component. Set up a new material balance to be used in calculating the associated values of a and b (Equation 5B). Determine the value of a corresponding to
Overhead 31.5 1.0
3.5/13.4 = 0.261 T c / T D = 2.33/20.3 = 0.1148; T c / T W = 2.33/0.261 = 8.93 U = (Knhk 0.1148 Kdk)/(0.8852) b = (8.93 K m i k - &,hk)/(7.93) = (100 66.9a)/(33.1) 3.02 2.02a
T,
-Above
Either of these expressions may be used to determine the quantity of the heavy key component in the distillate. T o determine the distribution of a third component a t minimum reflux, the method of procedure is similar to the determination of minimum reflux with only two distributed components. Following are the steps to be taken:
Feed 35.0 15.0 30.0 15.0 5.0
Feed-
d or w Kn or K m In 31.5 1.131 83.0 1.0 0.850 35.7 30.0 0.711 32.7 15.0 0.402 0.3 5.0 0.089 0 .4 158.1
---. Mole % 52.5 22.0 20.7 4.0 0.2
7 -
w 3.5 13.4 30.0 15.0 5.0
100'
-Below Kf7l
FeedZWB
1.340 123.8 1.020 53.1 0.711 02.7 0.402 21.4 0,089 5.4
Mole
% 40.5 19.9 23.6 8.1 2.0
266.4 1oo.o
At t, = 150" C. (302' F.), L, = 190.6 and 21, = 159.2, which differs little from ZL at 149' C. By interpolation L, = 158,3, a = 0.828, and Ln/D = 4.81/1. This value of 4.81 agrees well with 4.82 determined by vapor pressure data approximate method e method would probto illustrgte the compresent method, by own and Martin (1).
INDUSTRIAL AND ENGINEERING CHEMISTRY
1136
This is as close as can be expected, and it can be assumed that L,. = 445 M / H , whence L / D = 445/159.2 = 2.80/1. The same problem will now be solved by the method of Brown and Martin ( 1 ) . Although in their paper they used mole fractions, the same procedure can be followed with molal quantities. The method will be applied separately to the bottom and top sections of the tower: Below feed:
The method of Jenny (6) is omitted, not because of any errors in the derivation but because the other methods yield reasonably satisfactory results and are more straightforward. The problem is to determine the minimum reflux for the fractionation shown in the following table. Quantities are in moles per hour. The net overhead is to leave the reflux drum as a vapor. The operating pressure is 250 pounds per square inch gage:
c-1 c-2 c-3 c-4 c-5 C-6
Feed 13.7 30.0 116.2 299.0 156.0
Oveihead 13.7 30.0 114.0 1.5
721.9
159.2
107.0
rc = 116.2/299.0
=
Residue
.. .. ..
0.388;
TD
=
114.0/1.5 rw
rJrD
a =
=
0.388/76.0
( K n h ~
=
0.00511; rc/?w
- 0.00511 Knai.)/(0.995); b
0 = (721.9
- 562.7~)/(159.2)
=
=
Componelit w C-3 2.2 C-4 297.6 C-5 156.0 107.0 C-6 562.7
2.2 297.6 156.0 107.0 __ 562.7
... ... __
= 76.0; 2.2/297.5
=
=
179" F., a
=
0.738, b
=
Kno lm 283.8 1.86 595.0 0.939 0,447 205.0 0,210 1 2 0 . 2 1204,o v c = 0.476
t
220' F.. = 1120
=
Lm
Km 1.99
197.4
0.490 0.238
121.1
1.006
lrn
595.0
206.5
t = 215' F.,
Lm = Km 1.93 0.972 0.469 0,224
1120.0 rc = 0.330
1155 Zm
234.7 594.0 205.3
121.0
1155.0 F C = 0.396
By interpolation, LrrL= 1150, V = 587, b = 1.958, L,, = 428, u = 0.729, Ln/D = 2.69jl. Above feed :
52.5
t = 180' F.,
- 3.53~
Component d C-1 13.7 C-2 30.0 C-3 114.0 c-4 1 . 3 l59,2
A s s t m e t , = 180" F., a = 0.744, b = 1.90, t, = 211.6"F., L, = 436, L,,, = 1188, Zl,,= 450.4, Zl,, = 1166.5
Assume t,,
t = 210' F , L m = 1204
0.00740
(52.5 K,LL - K , , h k ) / ( 5 1 . 5 )
4.53
Vol. 33, No. 9
1.92, t,, = 213.4 L ,
=
449,
Ln
= 464
Km 15,s 4.22 1.54 0.749 7'0
t = 170' F.,
L n = 341
la
t
= 175' F., L n = 395
Kin In Kin 0.7 15.1 0.6 15.5 6.4 3.99 6.2 4.11 106.9 1.44 102.6 1.49 380.0 0.687 0.718 464.0 341.0 = 0.305 T c = 0 443 rc
231.6
In
0.7 6.2 104.9 283.2 395.0 = 0.370
L,,, = 1172 7 -
Component
c-1
Above Feed
d or w K n or Ktn 13.7 15.8 30.0 4.20
In
0 7 6.4
.-Mole % 0 2 1.4
Below Feed
w or (Iw
+ f)
14.4 36.4
KWZ
18.3
-In
1.5
bIolc
% 0.1
By interpolation, Ln = 383, 1' = 542, L / D = 2.40/1. (This method requires several trial calculations a t each temperature, and the final values are obtained by approximation. Thus, below the feed a t 210' F. calculations were made a t several values of L,, and it was indicated that the correct value a t that temperature was 1204. The values of I, were calculated by Equation 1B for components C-4, C-5, and C-6, and the value for C-3 was determined by diff erence.)
GASOLINE RECOVERY ASD STABILIZATION UNIT Courtesy, Arthur G. M c K s s & Cornpanu
The same problem will now be solved by the method of Gilliland (4). The values of a will be taken at 215" F. which is the feed plate temperature found by the present method. Molal quantities will be used rather than mole fractions: c-1 c-2 c-3 c-4 c-5 C-6 a
18.9
5.36
1.98
1.00
0.483
0.232
For case I:
.
A
(1/159.2)
I [(18.9)(13.7)/(17.9)] +
i(5.36) (30)/(4.36)1) = 0.322 B = (1/1562.7) ([(0.483) (156.0)/(1.497)] 4- [(0.232) (107.0)/ (1.748)] ) = 0.1148 =
Since B is smaller than A , Gilliland's Equation 9 should be used : C = (159.2/114.0) (0.98) = 1.369; 4 = 0.388 S = (562.7/159.2) (Ln/Ln 722) (1.98) M = [(114.0/0.388) - 1.5]/(0.98) (159.2) = 1.870 N = [(1.98) (0.388) 1.001 = 1.769
The present method yields a result which lies between those given by the assumption of constant composition in the feed zone and those given by consideration of only one section of the tower. This is in accord with Gilliland's statement (4) that Equations 9 and 10 give results that are too high and Equations 13 and 14 give results that are too low. EXAMPLE 3. This illustration is given to show the present method applied to the case of the distribution of three components. It is desired to fractionate the feed given below in such a manner that the residue will contain 0.2 mole of isobutane and 11.7 moles of isobutylene. It is desirable but not essential that all the n-butane be in the bottoms. Consequently, the initial solution is made on the assumption that all the n-butane is in the bottoms. The tower operates a t 7.0 atmospheres absolute. Quantities are in moles per hour:
+
+
Feed 5.0 17.9 29.6 39.4
CaHa
iso-C4Hla iso-GHa n-ChHlo iso-CaHn
I
127 L, = (L, =
468; a
=
rE
- 419) (L,+ 722)
TD TW rc/TD
0.745; L,/D = 2.94/1
L, = 491; a = 0.755; LJD = 3.08/1
I n the preceding calculations, certain minor terms of Gilliland's equations were neglected. Introduction of these terms makes no appreciable change in the results. For case 11:
+'
( B ) = 64.6/V
- (51.4/V) - (64.6/V)
+[ 299 + [: 5 116.2
=
1 1
-
'1 1
-1
(2*2) - 116.2 V 299 V (297.5)
- 7,490
+ 15,400
Above feed a t 215" F., assuming L, = 400,Cp' = 0.315:
M' = [(114/0.315) - 1.5]/(0.98) (159.2) = 2.305 N' = [(1.98) (0.315) 1.001 = 1.624 (LJ159.2)
+ + 1 = (2.305)
[1.624
+ (0.315) (1.370) (0.322)J =
4.06
L , = 487; a = 0.753; L,/D
=
0:2 11.7 39.4 0.4
40.6
51.j
- 51.7a)/(40.6)
=
Assumet, = 135"F., a = 0.799, b = 1.256, t, = 142.8"F.,
L, = 161.2, Lm = 253.5: ------Above Feedd or w K , or Km En 6.0 2.35 2.6 1.16 39.2 17.7 1.02 64.7 17.9 0.981 140.8 39.4 0.46 0.2 0.4 247.5
-Below w or
(.l a
Feed-
4-.. f)
7.6 0.2 11.7 39.4 0.4
Km
Zm
2.48 1.25 1.095 0.981 0.46
5.1 55.2 91.3 180.0 0.6
334.7
Since 21, is greater than L , the next trial should be made a t a higher valve of tn. However, it is found that a t no value of t, which is less than the.corresponding t,, is a satisfactory solution found. Since n-butane appears in considerable quantity in the values of both 1, and I,, it appears that it may be distributed between the overhead and residue. Consequently, Equation 10 is solved in such a way as to give the distribution of the heavy component. Assuming t, = 135" F.,
3.06/1
This value is much higher in comparison with the others than would be expected. Since the method is derived to be applied to conditions above the feed, it will be repeated a t 180' F. At this temperature A = 0.382, C = 1.475, M' = 1.559, N' = 1.889, and @' (at L, = 400) = 0.432. From these, L, = 368, a = 0.698, and L,/D = 2.31/1. Below feed a t 215" F., the values to use in Gilliland's Equation 14 are p = -1, and T = 0.526. The other values have been calculated above. From these, L, = 384, a = ~0.706,and L,/D = 2.41. Since Equation 13 allows for only those components found in the distillate, the minimum reflux ratio calculated therefrom at 215" F. is omitted from the table below. However, a difference of 35" F. made a difference of over 30 per cent in the value of the minimum reflux ratio: Method of Calculation Gilliland, Equation 10 Gilliland, Equation 9 Present method Brown and Martin, below feed Brown and iMartin. above feed Gilliland, Equation 14 Gilliland, Equation 13
.. ..
= 17.9/29.6 = 0.605 = 17.7/17.9 = 0.989 = 0.2/11.7 = 0.01710 0.605/0.989 = 0.612
CaHs iso-C4Hlo iso-ChHs n-C4Hio iso-CaH12
Ziyi = (159.2/V) ( A ) = 51.4/V = (562.7/V)
Residue
re/rw = 0.605/0.01710 = 35.4 a = (&,a - 0.612 Knrh)/(0.388) = (35.4 K,,tb - K,ik)/(34.4) = (92.3 b 2.272 - 1.272a
If Equation 10 is used,
Zhyh
Overhead 5.0 17.7 17.9
0.4 92.3
Substituting these values in Equation 9, L,
1137
INDUSTRIAL AND ENGINEERING CHEMISTRY
September, 1941
Minimum Reflux 3.08/1 2.94/1 2.80/1 2.69/1 2.40/1 2.41/1 2.31/1
ZD,,~
(0.670) (17.9)
o r -l D=h-k 17.7
LDhk
[
39.4 (17.9) 17.9 29.6
12.0
(F) (1:16 - 0.91) 17 7 1 1 6 - 1.02
= 12.0
The revised material balance is given below: Feed
6 = (92.3
- 39.7 a)/(52.6)
Overhead
=
1.755
Bottoms
- 0.755 a
At tn = 135" F., u = 0.799, b = 1.152, tm = 134.2'F. This indicates it is necessary to assume a lower temperature for tm.
INDUSTRIAL AND ENGINEERING CHEMISTRY
I138
Ah t, = 133’ F., u = 0.785, 6 = 1.163, t m = 134.S0F.,L n = 592.6, L, = 284.4: “1-
.. - __-
Mole
This result is reasonably satisfactory, and it can be assumed t h a t a = 195/247.6 = 0.787 or LID = 3.70/1. It appears from the results that slightly less than 12.0 moles per hour ,of n-butane will be in the overhead at minimum reflux. As a matter of interest, the value of T D X ~would have to be at least 11 X 14 X 29.6/14 X 25 X 17.9 = 0.727 in order to prevent n-butane from entering the overhead. I n the present case this would mean that the overhead would contain 24.3 moles per hour of isobutylene. The distribution for total reflux is calculated below, using values of a at 135” F.: ISo-CaHlo a
log 1.138
1 138
iso-C4Hs 1 00
log 1.270
n-CdHlo 0 893
-
ID
=
1.64;
Vol. 33, No. 9 lo =
1.73
These results, while not in extremely good agreement are within the slide-rule accuracy of the calculation. Comparing the results of the calculations on the basis of minimum reflux and total reflux, it appears that much more n-butane will be in the distillate in the former condition than in the latter. Since actual operations are usually carried out a t a reflux ratio close to the minimum, there will be an appreciable quantity of n-butane in the overhead from an operating tower. The empirical methods of obtaining actual decks for this case have not been fully tested, and plate-to-plate calculations are preferable.
Conclusion The approximate method of calculating the minimum reflux for multicomponent mixtures has been shown to yield results in good agreement with the results from plate-to-plate caloulatioris. It has also been shown to give results comparable with those of other methods but seemingly more accurate and to be applicable to the determination of the distribution of a third component of the feed. The fractionation a t total reflux is superior to that at minimum reflux as indicated by the comparative separations of the third component.
Literature Cited
log 1.117
(1) Brown, G. G., and M a r t i n , H. Z., Trans. Am. Inst. Chem. Engrs.. 35, 679 (1939). (2) Fenske, hf. It., IND.E N C . CHEM., 24, 482 (1932). (3) Gilliland, E. R., Ibid., 32, 918 (1940). (4) Ibid., 32, 1101 (1940). ( 5 ) Ibid., 32, 1220 (1940). (6) Jenny, F. J., Trans.A m Inst. Chem. Engrs., 35,635 (1939). (7) Robinson, C. S., and Gilliland, E. R., “Elements of Fractional Distlllatlon”, 3rd ed., p. 173, New York, MoGraw-Hi11 Book Co., 1939.
Nitration of Propane by Nitrogen Dioxide A careful study has been made of the nitra-
tion of propane by nitrogen dioxide over a wide temperature range i n order to compare this nitrating agent with nitric acid, which is employed commercially. Contrary to the reports of certain other investigators, nitrogen dioxide and nitric acid yield the same nitroparaffins although conversions are lower with the former reagent.
T
HE first vapor-phase nitration of z i saturated hydrocarThe. bon mas reported from this laboratory in 1934 (I) nitrating agent was nitric acid vapor. Sometime afterward, Urbanski and Slon (4) published a series of articles describing the nitration of methane, propane, %-pentane, n-hexane, n-heptane, n-octane, and n-nonane by nitrogen dioxide in the vapor phase in glass apparatus. Yields with methane were reported as “insignificant”, but the higher 1
Present address, Ethyl Gasoline Corporation, Baton Rouge. La.
v
H. B. HASS, JULIAN DORSKY‘, E. B. HODGE 0 Purdue University, Lafayette,
.4ND
Ind.
hydrocarbons were said to be converted to mixtures of monoand dinitroparaffins a t 200” C. in a ratio of about 60 to 40. Although minor amounts of secondary nitroparaffins were reported to be present, the principal products were believed to be the primary isomers, and such derivatives as 1,a-dinitropropane and 1,6-dinitrohexane were stated tocompose the main dinitro fractions. Since nylon could easily be made from I,& dinitrohexane by reducing one half to 1,6-hexanediamine, hydrolyzing the other half to adipic acid by the action of sulfuric acid, and condensing the amine and acid, it seemed that in spite of certain internal evidence of mistaken identification, the work of Urbanski and Slon would be worth verifying. [Urbanski and Slon reported that their “1-nitropropane” boiled a t 121“. 1-Kitropropane boils a t 132” while 2-nitropropane boils a t 120”. Similarly, they reported their
